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Fast design optimization of SLB dampers using FEM-calibrated surrogates:
hysteresis prediction with LSTM and damage-constrained optimization
Resumen y palabras clave
Abstract
Contexto: necesidad de optimización geométrica eficiente de disipadores SLB bajo cargas cíclicas.
Base: simulaciones FEM calibradas como ground truth para la respuesta histerética y variables internas de daño no directamente medibles.
Metodología:
generación de datasets FEM para disipadores con 2, 3 y 5 ventanas,
predicción de curvas histeréticas mediante modelos LSTM,
optimización geométrica mediante modelos surrogate supervisados y RBF,
comparación sistemática en términos de precisión y coste computacional.
Resultados clave: trade-off precisión–velocidad y recomendaciones prácticas.
Conclusión: viabilidad de pipelines rápidos y fiables para diseño asistido.
Keywords
hysteresis, LSTM, surrogate modeling, supervised learning, radial basis functions, structural optimization, FEM-calibrated models, shear-link dampers
1. Introducción
1.1 Motivación y problema de ingeniería
Disipadores SLB: maximizar disipación de energía y ductilidad, limitando daño local.
Limitaciones del ensayo experimental:
imposibilidad de acceder a variables internas,
alto coste para exploración geométrica.
Rol del FEM:
acceso a respuesta global e indicadores locales de daño,
generación sistemática de datos para optimización.
1.2 Retos principales
Respuesta histerética con memoria (dependencia del historial de carga).
Coste computacional elevado de simulaciones FEM.
Extrapolación limitada de modelos puramente basados en datos.
Necesidad de surrogates rápidos pero fiables.
1.3 Contribuciones del artículo
Generación de datasets FEM para disipadores con distinta complejidad geométrica.
Predicción de curvas histeréticas mediante LSTM.
Optimización geométrica basada en:
modelos ML supervisados (RF, GBT, XGBoost, SVR, MLP),
Radial Basis Functions.
Comparativa exhaustiva precisión vs tiempo.
Estrategia de validación y realimentación adaptativa.
2. Simulación numérica y generación del ground truth
Esta sección queda muy bien enfocada en tu esquema; solo la estructuro mejor.
2.1 Geometría de los disipadores
Disipadores SLB con:
2 ventanas,
3 ventanas,
5 ventanas.
Parámetros geométricos:
espesores de ventanas (tw),
espesor de marco (tf).
2.2 Protocolos de carga cíclica
Desplazamiento impuesto por actuador.
Protocolos de amplitud progresiva.
Dependencia del protocolo con la altura del disipador.
2.3 Variables de salida del FEM (QoIs)
Respuesta global: curva fuerza–desplazamiento (histéresis).
Indicadores de daño:
TFDMap,
distorsión local asociada a la disipación de energía.
2.4 Diseño del conjunto de simulaciones
Exploración sistemática del espacio de diseño.
Muestreo cuasi-aleatorio de parámetros geométricos.
Separación clara entre:
datasets de entrenamiento,
casos de validación.
3. Predicción de curvas histeréticas mediante LSTM
Esta sección queda muy sólida y es uno de los puntos fuertes del paper.
3.1 Formulación del problema con memoria
Objetivo: predecir
F(t)
F(t) a partir del historial de desplazamiento y geometría.
Justificación:
el desplazamiento instantáneo no es suficiente,
dependencia del sentido y amplitud previa de carga.
3.2 Representación secuencial de la señal
Entrada:
xt=[ut,u˙t,ciclo,amplitud,paraˊmetros geomeˊtricos]
x
t
​
=[u
t
​
,
u
˙
t
​
,ciclo,amplitud,par
a
ˊ
metros geom
e
ˊ
tricos]
Salida:
Ft
F
t
​
(autoregresivo) o
secuencia completa (many-to-many).
3.3 Arquitecturas LSTM consideradas
LSTM many-to-many.
Encoder–decoder para generalización entre protocolos.
LSTM con atención (opcional).
3.4 Entrenamiento y validación
Normalización.
Funciones de pérdida (MAE/MSE + penalización en picos).
División por simulaciones completas (evitar data leakage).
3.5 Ventajas y limitaciones
Ventajas: captura explícita de memoria, alta fidelidad en histéresis.
Limitaciones: coste de entrenamiento, necesidad de datos, extrapolación.
4. Optimización geométrica basada en modelos surrogate
4.1 Formulación del problema
Variables de diseño:
{twi,tf}
{tw
i
​
,tf}.
Objetivos:
minimizar daño,
maximizar distorsión / disipación de energía.
Restricciones basadas en indicadores de daño.
4.2 Surrogates empleados
Modelos supervisados: RF, GBT, XGBoost, SVR, MLP.
Radial Basis Functions como alternativa directa.
4.3 Algoritmo de optimización
Differential Evolution (DE).
Evaluación masiva mediante surrogates.
Selección de geometrías óptimas candidatas.
5. Validación numérica y realimentación adaptativa
5.1 Validación FEM de diseños optimizados
Comparación surrogate vs FEM:
curva histerética,
indicadores de daño.
5.2 Estrategia de reentrenamiento
Criterio de error admisible.
Incorporación iterativa de nuevas simulaciones FEM.
6. Comparativa: modelos supervisados vs RBF
Esta sección es clave y merece entidad propia.
6.1 Precisión predictiva
Error en daño.
Error en variables de desempeño.
6.2 Coste computacional
Tiempo de entrenamiento.
Tiempo de inferencia.
Escalabilidad con la dimensión del problema.
6.3 Discusión práctica
Cuándo usar cada enfoque según:
tamaño del dataset,
dimensionalidad,
necesidad de rapidez.
7. Discusión
Trade-off precisión–velocidad–robustez.
Papel del feature engineering frente a métodos puramente interpolativos.
LSTM como herramienta complementaria, no sustituta, del surrogate para optimización.
Implicaciones para diseño asistido en ingeniería estructural.
8. Conclusiones
FEM como generador de ground truth rico.
LSTM eficaz para histéresis con memoria.
Optimización acelerada viable con surrogates.
RBF como solución ultra-rápida en dominios bien cubiertos.
Recomendaciones claras según escenario de uso.
Apéndices
A. Detalles de normalización y métricas.
B. Hiperparámetros LSTM.
C. Definición matemática de la función objetivo.
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...@@ -3,7 +3,7 @@ ...@@ -3,7 +3,7 @@
\usepackage{colortbl} \usepackage{colortbl}
\usepackage{xcolor} \usepackage{xcolor}
\usepackage{steinmetz} \usepackage{steinmetz}
\graphicspath{{../Figures/}{./images/}} \graphicspath{{./images/}}
% Own definitions % Own definitions
\newcommand{\tb}[1]{\textbf{#1}} \newcommand{\tb}[1]{\textbf{#1}}
...@@ -129,7 +129,7 @@ Figure \ref{fig:MethodologyFlowChart} summarizes the proposed workflow. The diff ...@@ -129,7 +129,7 @@ Figure \ref{fig:MethodologyFlowChart} summarizes the proposed workflow. The diff
\begin{figure*}[htbp] \begin{figure*}[htbp]
\centering \centering
\includegraphics[width=0.75\textwidth]{../Figures/MethodologyFlowChart.pdf} \includegraphics[width=0.75\textwidth]{./images/MethodologyFlowChart/MethodologyFlowChart.pdf}
\caption{Flow chart of the proposed adaptive surrogate-assisted optimization framework.} \caption{Flow chart of the proposed adaptive surrogate-assisted optimization framework.}
\label{fig:MethodologyFlowChart} \label{fig:MethodologyFlowChart}
\end{figure*} \end{figure*}
...@@ -140,7 +140,7 @@ The BDSL dampers analysed in this work, with one representative configuration sh ...@@ -140,7 +140,7 @@ The BDSL dampers analysed in this work, with one representative configuration sh
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.25\textwidth]{../Figures/Device.png} \includegraphics[width=0.25\textwidth]{./images/Device.png}
\caption{Representative BDSL damper configuration considered in the optimization.} \caption{Representative BDSL damper configuration considered in the optimization.}
\label{fig:Device} \label{fig:Device}
\end{figure} \end{figure}
...@@ -156,7 +156,7 @@ where $N_w$ denotes the number of windows. The device width and height are ident ...@@ -156,7 +156,7 @@ where $N_w$ denotes the number of windows. The device width and height are ident
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.40\textwidth]{../Figures/DeviceGeom.pdf} \includegraphics[width=0.40\textwidth]{./images/DeviceGeom/DeviceGeom.pdf}
\caption{Geometric scheme of a representative BDSL device considered in this study.} \caption{Geometric scheme of a representative BDSL device considered in this study.}
\label{fig:DeviceGeom} \label{fig:DeviceGeom}
\end{figure} \end{figure}
...@@ -182,7 +182,7 @@ $F_5$ & 2.00 & 1.17 & 5 & $t_{w,1},\ldots,t_{w,5}$ & 5--12 mm \\ ...@@ -182,7 +182,7 @@ $F_5$ & 2.00 & 1.17 & 5 & $t_{w,1},\ldots,t_{w,5}$ & 5--12 mm \\
\section{Validation of the FEM numerical model}\label{sec:fem} \section{Validation of the FEM numerical model}\label{sec:fem}
The surrogate models developed in this work were trained using data generated from three-dimensional FEM simulations. The numerical model is based on a previously calibrated and validated representation of the BDSL device, described in detail in Ramirez et al. \cite{RamirezMachado2025}. An example of the numerical setup is shown in Figure \ref{fig:FEMsetup}. The simulations were carried out using the COMPACK code, an explicit dynamic FEM solver for linear and nonlinear problems \cite{Martinez2011}. The model accounts for large displacements, material and geometric nonlinearities, contact interactions and the boundary conditions associated with the experimental configuration. The surrogate models developed in this work were trained using data generated from three-dimensional FEM simulations. The numerical model is based on a previously calibrated and validated representation of the BDSL device, described in detail in Ramirez et al. \cite{RamirezMachado2025}. An example of the numerical setup is shown in Figure \ref{fig:FEMSetup}. The simulations were carried out using the COMPACK code, an explicit dynamic FEM solver for linear and nonlinear problems \cite{Martinez2011}. The model accounts for large displacements, material and geometric nonlinearities, contact interactions and the boundary conditions associated with the experimental configuration.
The dissipative steel component is modelled as ASTM A36 steel, whose cyclic plastic behaviour is represented by the Yoshida--Uemori model \cite{Yoshida2002,Jia2014}. This constitutive law allows the model to reproduce cyclic hardening, softening and Bauschinger-type effects under large plastic deformation. The steel component is discretized using linear eight-node hexahedral solid elements, providing a structured three-dimensional mesh suitable for extracting local stress, strain and damage-related fields. The dissipative steel component is modelled as ASTM A36 steel, whose cyclic plastic behaviour is represented by the Yoshida--Uemori model \cite{Yoshida2002,Jia2014}. This constitutive law allows the model to reproduce cyclic hardening, softening and Bauschinger-type effects under large plastic deformation. The steel component is discretized using linear eight-node hexahedral solid elements, providing a structured three-dimensional mesh suitable for extracting local stress, strain and damage-related fields.
...@@ -190,16 +190,16 @@ The imposed displacement is applied through an actuator-like connector that tran ...@@ -190,16 +190,16 @@ The imposed displacement is applied through an actuator-like connector that tran
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.495\textwidth]{../Figures/FEMsetup.pdf} \includegraphics[width=0.495\textwidth]{./images/FEMSetup/FEMSetup.pdf}
\caption{FEM validation model of the BDSL device: mesh discretization, main components, boundary conditions and local/global buckling control.} \caption{FEM validation model of the BDSL device: mesh discretization, main components, boundary conditions and local/global buckling control.}
\label{fig:FEMsetup} \label{fig:FEMSetup}
\end{figure} \end{figure}
The model was calibrated and validated against cyclic experimental tests performed on representative BDSL specimens. The calibration involved the material parameters, assembled geometry, contact definitions, support flexibility and boundary conditions. The validated model accurately reproduces the main global experimental responses. Figure \ref{fig:FEM_validation_comparison} shows the comparison between experimental and numerical results, confirming the suitability of the FEM model as a numerical reference for configurations beyond those experimentally tested. The model was calibrated and validated against cyclic experimental tests performed on representative BDSL specimens. The calibration involved the material parameters, assembled geometry, contact definitions, support flexibility and boundary conditions. The validated model accurately reproduces the main global experimental responses. Figure \ref{fig:FEM_validation_comparison} shows the comparison between experimental and numerical results, confirming the suitability of the FEM model as a numerical reference for configurations beyond those experimentally tested.
\begin{figure*}[htbp] \begin{figure*}[htbp]
\centering \centering
\includegraphics[width=0.80\textwidth]{../Figures/plot_FEM_validation/FEM_validation_comparison.png} \includegraphics[width=0.80\textwidth]{./images/PlotFEMValidation/FEM_validation_comparison.pdf}
\caption{Experimental--numerical validation of the BDSL model: hysteretic response (left) and cumulative dissipated energy (right).} \caption{Experimental--numerical validation of the BDSL model: hysteretic response (left) and cumulative dissipated energy (right).}
\label{fig:FEM_validation_comparison} \label{fig:FEM_validation_comparison}
\end{figure*} \end{figure*}
...@@ -239,7 +239,7 @@ For every sampled configuration, a FEM simulation is performed under a displacem ...@@ -239,7 +239,7 @@ For every sampled configuration, a FEM simulation is performed under a displacem
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.495\textwidth]{../Figures/LoadPatterns/LoadPatterns.png} \includegraphics[width=0.495\textwidth]{./images/LoadPatterns/LoadPatterns.pdf}
\caption{Displacement-controlled cyclic loading patterns adopted for the different device heights considered in the FEM campaign.} \caption{Displacement-controlled cyclic loading patterns adopted for the different device heights considered in the FEM campaign.}
\label{fig:LoadPatterns} \label{fig:LoadPatterns}
\end{figure} \end{figure}
...@@ -262,7 +262,7 @@ Model selection is performed in two stages. First, for each candidate algorithm, ...@@ -262,7 +262,7 @@ Model selection is performed in two stages. First, for each candidate algorithm,
\begin{figure*}[htbp] \begin{figure*}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{../Figures/BayesianSearchCV.pdf} \includegraphics[width=1.0\textwidth]{./images/BayesianSearchCV/BayesianSearchCV.pdf}
\caption{Workflow of the supervised surrogate training and selection strategy. For each output variable, the cross-validation strategy is adapted to the dataset size, Bayesian optimization is used to tune each candidate model and the final surrogate is selected according to RMSE accuracy and fold-wise RMSE dispersion.} \caption{Workflow of the supervised surrogate training and selection strategy. For each output variable, the cross-validation strategy is adapted to the dataset size, Bayesian optimization is used to tune each candidate model and the final surrogate is selected according to RMSE accuracy and fold-wise RMSE dispersion.}
\label{fig:BayesianSearchCV} \label{fig:BayesianSearchCV}
\end{figure*} \end{figure*}
...@@ -323,7 +323,7 @@ The surrogate-optimized geometry is not accepted directly. Instead, once an opti ...@@ -323,7 +323,7 @@ The surrogate-optimized geometry is not accepted directly. Instead, once an opti
\begin{figure*}[htbp] \begin{figure*}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{../Figures/OptimizationFlowChart.pdf} \includegraphics[width=1.0\textwidth]{./images/OptimizationFlowChart/OptimizationFlowChart.pdf}
\caption{Surrogate-assisted optimization and FEM validation retraining loop.} \caption{Surrogate-assisted optimization and FEM validation retraining loop.}
\label{fig:OptimizationFlowChart} \label{fig:OptimizationFlowChart}
\end{figure*} \end{figure*}
...@@ -334,7 +334,7 @@ The supervised-learning comparison shows a clear hierarchy among the candidate s ...@@ -334,7 +334,7 @@ The supervised-learning comparison shows a clear hierarchy among the candidate s
\begin{figure*}[htbp] \begin{figure*}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{../Figures/MLSurrogatesComparison/surrogate_selection_summary_barplot.png} \includegraphics[width=1.0\textwidth]{./images/MLSurrogatesComparison/surrogate_selection_summary_barplot.pdf}
\caption{Summary of the supervised surrogate selection over all geometry families, adaptive iterations and target outputs. The training time corresponds to the median time required for one Bayesian hyperparameter search for a single output variable and, for visualization purposes, is in logarithmic scale.} \caption{Summary of the supervised surrogate selection over all geometry families, adaptive iterations and target outputs. The training time corresponds to the median time required for one Bayesian hyperparameter search for a single output variable and, for visualization purposes, is in logarithmic scale.}
\label{fig:surrogate_selection_summary_barplot} \label{fig:surrogate_selection_summary_barplot}
\end{figure*} \end{figure*}
...@@ -405,7 +405,7 @@ Figure~\ref{fig:optimized_window_thickness_evolution} shows the evolution of the ...@@ -405,7 +405,7 @@ Figure~\ref{fig:optimized_window_thickness_evolution} shows the evolution of the
\begin{figure*}[htbp] \begin{figure*}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{../Figures/OptimizedWindowThicknessEvolution/optimized_window_thickness_evolution.png} \includegraphics[width=1.0\textwidth]{./images/OptimizedWindowThicknessEvolution/optimized_window_thickness_evolution.pdf}
\caption{Evolution of the optimized window thicknesses during the adaptive optimization process.} \caption{Evolution of the optimized window thicknesses during the adaptive optimization process.}
\label{fig:optimized_window_thickness_evolution} \label{fig:optimized_window_thickness_evolution}
\end{figure*} \end{figure*}
...@@ -418,7 +418,7 @@ This behaviour is illustrated in Figure~\ref{fig:rbf_surface_evolution}, which s ...@@ -418,7 +418,7 @@ This behaviour is illustrated in Figure~\ref{fig:rbf_surface_evolution}, which s
\begin{figure*}[htbp] \begin{figure*}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{../Figures/RBFOptimizationSurfaceEvolution/rbf_surface_evolution.png} \includegraphics[width=1.0\textwidth]{./images/RBFOptimizationSurfaceEvolution/rbf_surface_evolution.pdf}
\caption{Evolution of the RBF objective surface during the adaptive optimization process for the two-window families. Left: $F_1$. Right: $F_2$.} \caption{Evolution of the RBF objective surface during the adaptive optimization process for the two-window families. Left: $F_1$. Right: $F_2$.}
\label{fig:rbf_surface_evolution} \label{fig:rbf_surface_evolution}
\end{figure*} \end{figure*}
...@@ -456,7 +456,7 @@ None reported. ...@@ -456,7 +456,7 @@ None reported.
The authors declare no potential conflict of interests. The authors declare no potential conflict of interests.
\bibliography{../wileyNJD-AMA} \bibliography{./wileyNJD-AMA}
\bmsection*{Supporting information} \bmsection*{Supporting information}
......
\documentclass[AMA,Times1COL]{WileyNJDv5} %STIX1COL,STIX2COL,STIXSMALL \documentclass[AMA,Times1COL]{../WileyNJDv5} %STIX1COL,STIX2COL,STIXSMALL
% Own definitions % Own definitions
\newcommand{\tb}[1]{\textbf{#1}} \newcommand{\tb}[1]{\textbf{#1}}
...@@ -87,7 +87,7 @@ Figure \ref{fig:MethodologyFlowChart} summarizes the proposed workflow. The diff ...@@ -87,7 +87,7 @@ Figure \ref{fig:MethodologyFlowChart} summarizes the proposed workflow. The diff
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.75\textwidth]{./Figures/MethodologyFlowChart.pdf} \includegraphics[width=0.75\textwidth]{../Figures/MethodologyFlowChart.pdf}
\caption{Flow chart of the proposed adaptive surrogate-assisted optimization framework.} \caption{Flow chart of the proposed adaptive surrogate-assisted optimization framework.}
\label{fig:MethodologyFlowChart} \label{fig:MethodologyFlowChart}
\end{figure} \end{figure}
...@@ -98,7 +98,7 @@ The BDSL dampers analysed in this work, with one representative configuration sh ...@@ -98,7 +98,7 @@ The BDSL dampers analysed in this work, with one representative configuration sh
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.25\textwidth]{./Figures/Device.png} \includegraphics[width=0.25\textwidth]{../Figures/Device.png}
\caption{Representative BDSL damper configuration considered in the optimization.} \caption{Representative BDSL damper configuration considered in the optimization.}
\label{fig:Device} \label{fig:Device}
\end{figure} \end{figure}
...@@ -114,11 +114,11 @@ where $W$ denotes the number of windows. The width and height identifiers of the ...@@ -114,11 +114,11 @@ where $W$ denotes the number of windows. The width and height identifiers of the
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.15\textwidth]{Figures/H30_B29.png}\label{fig:H30_B29} \includegraphics[width=0.15\textwidth]{../Figures/H30_B29.png}\label{fig:H30_B29}
\includegraphics[width=0.15\textwidth]{Figures/H30_B34.png}\label{fig:H30_B34} \includegraphics[width=0.15\textwidth]{../Figures/H30_B34.png}\label{fig:H30_B34}
\includegraphics[width=0.15\textwidth]{Figures/H45_B29.png}\label{fig:H45_B29} \includegraphics[width=0.15\textwidth]{../Figures/H45_B29.png}\label{fig:H45_B29}
\includegraphics[width=0.15\textwidth]{Figures/H45_B34.png}\label{fig:H45_B34} \includegraphics[width=0.15\textwidth]{../Figures/H45_B34.png}\label{fig:H45_B34}
\includegraphics[width=0.15\textwidth]{Figures/H60_B34.png}\label{fig:H60_B34} \includegraphics[width=0.15\textwidth]{../Figures/H60_B34.png}\label{fig:H60_B34}
\caption{BDSL families considered for optimization in the current study. From left to right: H30\_B29, H30\_B34, H45\_B29, H45\_B34 and H60\_B34.} \caption{BDSL families considered for optimization in the current study. From left to right: H30\_B29, H30\_B34, H45\_B29, H45\_B34 and H60\_B34.}
\label{fig:GeometryFamilies} \label{fig:GeometryFamilies}
\end{figure} \end{figure}
...@@ -152,7 +152,7 @@ The imposed displacement is applied through an actuator-like connector that tran ...@@ -152,7 +152,7 @@ The imposed displacement is applied through an actuator-like connector that tran
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.60\textwidth]{./Figures/FEMsetup.png} \includegraphics[width=0.60\textwidth]{../Figures/FEMsetup.png}
\caption{FEM validation model of the BDSL device: mesh discretization, main components, boundary conditions and local/global buckling control.} \caption{FEM validation model of the BDSL device: mesh discretization, main components, boundary conditions and local/global buckling control.}
\label{fig:FEMsetup} \label{fig:FEMsetup}
\end{figure} \end{figure}
...@@ -161,7 +161,7 @@ The model was calibrated and validated against cyclic experimental tests perform ...@@ -161,7 +161,7 @@ The model was calibrated and validated against cyclic experimental tests perform
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.80\textwidth]{./Figures/plot_FEM_validation/FEM_validation_comparison.png} \includegraphics[width=0.80\textwidth]{../Figures/plot_FEM_validation/FEM_validation_comparison.png}
\caption{Experimental--numerical validation of the BDSL model: hysteretic response (left) and cumulative dissipated energy (right).} \caption{Experimental--numerical validation of the BDSL model: hysteretic response (left) and cumulative dissipated energy (right).}
\label{fig:FEM_validation_comparison} \label{fig:FEM_validation_comparison}
\end{figure} \end{figure}
...@@ -201,7 +201,7 @@ For every sampled configuration, a FEM simulation is performed under a displacem ...@@ -201,7 +201,7 @@ For every sampled configuration, a FEM simulation is performed under a displacem
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=0.50\textwidth]{./Figures/LoadPatterns/LoadPatterns.png} \includegraphics[width=0.50\textwidth]{../Figures/LoadPatterns/LoadPatterns.png}
\caption{Displacement-controlled cyclic loading patterns adopted for the different device heights considered in the FEM campaign.} \caption{Displacement-controlled cyclic loading patterns adopted for the different device heights considered in the FEM campaign.}
\label{fig:LoadPatterns} \label{fig:LoadPatterns}
\end{figure} \end{figure}
...@@ -297,7 +297,7 @@ Model selection is performed in two stages. First, for each candidate algorithm, ...@@ -297,7 +297,7 @@ Model selection is performed in two stages. First, for each candidate algorithm,
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{./Figures/BayesianSearchCV.pdf} \includegraphics[width=1.0\textwidth]{../Figures/BayesianSearchCV.pdf}
\caption{Workflow of the supervised surrogate training and selection strategy. For each output variable, the cross-validation strategy is adapted to the dataset size, Bayesian optimization is used to tune each candidate model and the final surrogate is selected according to RMSE accuracy and fold-wise RMSE dispersion.} \caption{Workflow of the supervised surrogate training and selection strategy. For each output variable, the cross-validation strategy is adapted to the dataset size, Bayesian optimization is used to tune each candidate model and the final surrogate is selected according to RMSE accuracy and fold-wise RMSE dispersion.}
\label{fig:BayesianSearchCV} \label{fig:BayesianSearchCV}
\end{figure} \end{figure}
...@@ -375,7 +375,7 @@ The surrogate-optimized geometry is not accepted directly. Instead, once an opti ...@@ -375,7 +375,7 @@ The surrogate-optimized geometry is not accepted directly. Instead, once an opti
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{./Figures/OptimizationFlowChart.pdf} \includegraphics[width=1.0\textwidth]{../Figures/OptimizationFlowChart.pdf}
\caption{Surrogate-assisted optimization and FEM validation retraining loop.} \caption{Surrogate-assisted optimization and FEM validation retraining loop.}
\label{fig:OptimizationFlowChart} \label{fig:OptimizationFlowChart}
\end{figure} \end{figure}
...@@ -386,7 +386,7 @@ The supervised-learning comparison shows a clear hierarchy among the candidate s ...@@ -386,7 +386,7 @@ The supervised-learning comparison shows a clear hierarchy among the candidate s
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{./Figures/MLSurrogatesComparison/surrogate_selection_summary_barplot.png} \includegraphics[width=1.0\textwidth]{../Figures/MLSurrogatesComparison/surrogate_selection_summary_barplot.png}
\caption{Summary of the supervised surrogate selection over all geometry families, adaptive iterations and target outputs. The training time corresponds to the median time required for one Bayesian hyperparameter search for a single output variable and, for visualization purposes, is in logarithmic scale.} \caption{Summary of the supervised surrogate selection over all geometry families, adaptive iterations and target outputs. The training time corresponds to the median time required for one Bayesian hyperparameter search for a single output variable and, for visualization purposes, is in logarithmic scale.}
\label{fig:surrogate_selection_summary_barplot} \label{fig:surrogate_selection_summary_barplot}
\end{figure} \end{figure}
...@@ -457,7 +457,7 @@ Figure~\ref{fig:optimized_window_thickness_evolution} shows the evolution of the ...@@ -457,7 +457,7 @@ Figure~\ref{fig:optimized_window_thickness_evolution} shows the evolution of the
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{./Figures/OptimizedWindowThicknessEvolution/optimized_window_thickness_evolution.png} \includegraphics[width=1.0\textwidth]{../Figures/OptimizedWindowThicknessEvolution/optimized_window_thickness_evolution.png}
\caption{Evolution of the optimized window thicknesses during the adaptive optimization process.} \caption{Evolution of the optimized window thicknesses during the adaptive optimization process.}
\label{fig:optimized_window_thickness_evolution} \label{fig:optimized_window_thickness_evolution}
\end{figure} \end{figure}
...@@ -470,7 +470,7 @@ This behaviour is illustrated in Figure~\ref{fig:rbf_surface_evolution}, which s ...@@ -470,7 +470,7 @@ This behaviour is illustrated in Figure~\ref{fig:rbf_surface_evolution}, which s
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[width=1.0\textwidth]{./Figures/RBFOptimizationSurfaceEvolution/rbf_surface_evolution.png} \includegraphics[width=1.0\textwidth]{../Figures/RBFOptimizationSurfaceEvolution/rbf_surface_evolution.png}
\caption{Evolution of the RBF objective surface during the adaptive optimization process for the two-window families. Left: H30\_B29. Right: H30\_B34.} \caption{Evolution of the RBF objective surface during the adaptive optimization process for the two-window families. Left: H30\_B29. Right: H30\_B34.}
\label{fig:rbf_surface_evolution} \label{fig:rbf_surface_evolution}
\end{figure} \end{figure}
...@@ -508,7 +508,7 @@ None reported. ...@@ -508,7 +508,7 @@ None reported.
The authors declare no potential conflict of interests. The authors declare no potential conflict of interests.
\bibliography{wileyNJD-AMA} \bibliography{../wileyNJD-AMA}
\bmsection*{Supporting information} \bmsection*{Supporting information}
......
...@@ -8,7 +8,7 @@ ...@@ -8,7 +8,7 @@
%% This is a generated file. %% This is a generated file.
%% %%
%% Copyright (C) 1994-2004 Peter Williams <pwil3058@bigpond.net.au> %% Copyright (C) 1994-2004 Peter Williams <pwil3058@bigpond.net.au>
%% Copyright (C) 2005-2009 Rogrio Brito <rbrito@ime.usp.br> %% Copyright (C) 2005-2009 Rogério Brito <rbrito@ime.usp.br>
%% %%
%% This document file is free software; you can redistribute it and/or %% This document file is free software; you can redistribute it and/or
%% modify it under the terms of the GNU Lesser General Public License as %% modify it under the terms of the GNU Lesser General Public License as
......
family,height_cm,width_cm,surrogate,iteration,source_model,window,window_index,thickness_mm,objective_surrogate family,height_cm,width_cm,surrogate,iteration,source_model,window,window_index,thickness_mm,objective_surrogate
H30_B29,30,29,RBF,1,opt1,tw1,1,12.34,0.0 H30_B29,30,29,RBF,1,opt1,tw1,1,12.34,0.0
H30_B29,30,29,RBF,1,opt1,tw2,2,14.34,0.0 H30_B29,30,29,RBF,1,opt1,tw2,2,14.34,0.0
H30_B29,30,29,RBF,2,opt2,tw1,1,12.68,0.0 H30_B29,30,29,RBF,2,opt2,tw1,1,12.68,0.0
H30_B29,30,29,RBF,2,opt2,tw2,2,14.91,0.0 H30_B29,30,29,RBF,2,opt2,tw2,2,14.91,0.0
H30_B29,30,29,RBF,3,opt3,tw1,1,12.56,0.0 H30_B29,30,29,RBF,3,opt3,tw1,1,12.56,0.0
H30_B29,30,29,RBF,3,opt3,tw2,2,14.79,0.0 H30_B29,30,29,RBF,3,opt3,tw2,2,14.79,0.0
H30_B29,30,29,Supervised ML,1,opt1,tw1,1,12.6,0.0 H30_B29,30,29,Supervised ML,1,opt1,tw1,1,12.6,0.0
H30_B29,30,29,Supervised ML,1,opt1,tw2,2,14.64,0.0 H30_B29,30,29,Supervised ML,1,opt1,tw2,2,14.64,0.0
H30_B29,30,29,Supervised ML,2,opt2,tw1,1,12.53,0.0 H30_B29,30,29,Supervised ML,2,opt2,tw1,1,12.53,0.0
H30_B29,30,29,Supervised ML,2,opt2,tw2,2,14.75,0.0 H30_B29,30,29,Supervised ML,2,opt2,tw2,2,14.75,0.0
H30_B34,30,34,RBF,1,opt1,tw1,1,15.5,507.37762 H30_B34,30,34,RBF,1,opt1,tw1,1,15.5,507.37762
H30_B34,30,34,RBF,1,opt1,tw2,2,20.0,507.37762 H30_B34,30,34,RBF,1,opt1,tw2,2,20.0,507.37762
H30_B34,30,34,RBF,2,opt2,tw1,1,14.8,700.7361 H30_B34,30,34,RBF,2,opt2,tw1,1,14.8,700.7361
H30_B34,30,34,RBF,2,opt2,tw2,2,18.93,700.7361 H30_B34,30,34,RBF,2,opt2,tw2,2,18.93,700.7361
H30_B34,30,34,RBF,3,opt3,tw1,1,14.77,688.53041 H30_B34,30,34,RBF,3,opt3,tw1,1,14.77,688.53041
H30_B34,30,34,RBF,3,opt3,tw2,2,18.95,688.53041 H30_B34,30,34,RBF,3,opt3,tw2,2,18.95,688.53041
H30_B34,30,34,Supervised ML,1,opt1,tw1,1,15.69,541.94744 H30_B34,30,34,Supervised ML,1,opt1,tw1,1,15.69,541.94744
H30_B34,30,34,Supervised ML,1,opt1,tw2,2,20.0,541.94744 H30_B34,30,34,Supervised ML,1,opt1,tw2,2,20.0,541.94744
H30_B34,30,34,Supervised ML,2,opt2,tw1,1,15.14,830.19116 H30_B34,30,34,Supervised ML,2,opt2,tw1,1,15.14,830.19116
H30_B34,30,34,Supervised ML,2,opt2,tw2,2,20.0,830.19116 H30_B34,30,34,Supervised ML,2,opt2,tw2,2,20.0,830.19116
H30_B34,30,34,Supervised ML,3,opt3,tw1,1,15.2,796.29365 H30_B34,30,34,Supervised ML,3,opt3,tw1,1,15.2,796.29365
H30_B34,30,34,Supervised ML,3,opt3,tw2,2,20.0,796.29365 H30_B34,30,34,Supervised ML,3,opt3,tw2,2,20.0,796.29365
H45_B29,45,29,RBF,1,opt1,tw1,1,5.94,0.0 H45_B29,45,29,RBF,1,opt1,tw1,1,5.94,0.0
H45_B29,45,29,RBF,1,opt1,tw2,2,8.38,0.0 H45_B29,45,29,RBF,1,opt1,tw2,2,8.38,0.0
H45_B29,45,29,RBF,1,opt1,tw3,3,9.28,0.0 H45_B29,45,29,RBF,1,opt1,tw3,3,9.28,0.0
H45_B29,45,29,RBF,2,opt2,tw1,1,5.69,0.0 H45_B29,45,29,RBF,2,opt2,tw1,1,5.69,0.0
H45_B29,45,29,RBF,2,opt2,tw2,2,7.97,0.0 H45_B29,45,29,RBF,2,opt2,tw2,2,7.97,0.0
H45_B29,45,29,RBF,2,opt2,tw3,3,9.02,0.0 H45_B29,45,29,RBF,2,opt2,tw3,3,9.02,0.0
H45_B29,45,29,RBF,3,opt3,tw1,1,5.81,0.0 H45_B29,45,29,RBF,3,opt3,tw1,1,5.81,0.0
H45_B29,45,29,RBF,3,opt3,tw2,2,7.88,0.0 H45_B29,45,29,RBF,3,opt3,tw2,2,7.88,0.0
H45_B29,45,29,RBF,3,opt3,tw3,3,8.98,0.0 H45_B29,45,29,RBF,3,opt3,tw3,3,8.98,0.0
H45_B29,45,29,Supervised ML,1,opt1,tw1,1,5.96,0.0 H45_B29,45,29,Supervised ML,1,opt1,tw1,1,5.96,0.0
H45_B29,45,29,Supervised ML,1,opt1,tw2,2,8.23,0.0 H45_B29,45,29,Supervised ML,1,opt1,tw2,2,8.23,0.0
H45_B29,45,29,Supervised ML,1,opt1,tw3,3,9.47,0.0 H45_B29,45,29,Supervised ML,1,opt1,tw3,3,9.47,0.0
H45_B29,45,29,Supervised ML,2,opt2,tw1,1,5.7,0.0 H45_B29,45,29,Supervised ML,2,opt2,tw1,1,5.7,0.0
H45_B29,45,29,Supervised ML,2,opt2,tw2,2,7.9,0.0 H45_B29,45,29,Supervised ML,2,opt2,tw2,2,7.9,0.0
H45_B29,45,29,Supervised ML,2,opt2,tw3,3,9.02,0.0 H45_B29,45,29,Supervised ML,2,opt2,tw3,3,9.02,0.0
H45_B29,45,29,Supervised ML,3,opt3,tw1,1,5.72,0.0 H45_B29,45,29,Supervised ML,3,opt3,tw1,1,5.72,0.0
H45_B29,45,29,Supervised ML,3,opt3,tw2,2,7.87,0.0 H45_B29,45,29,Supervised ML,3,opt3,tw2,2,7.87,0.0
H45_B29,45,29,Supervised ML,3,opt3,tw3,3,8.96,0.0 H45_B29,45,29,Supervised ML,3,opt3,tw3,3,8.96,0.0
H45_B34,45,34,RBF,1,opt1,tw1,1,7.21,0.0 H45_B34,45,34,RBF,1,opt1,tw1,1,7.21,0.0
H45_B34,45,34,RBF,1,opt1,tw2,2,9.27,0.0 H45_B34,45,34,RBF,1,opt1,tw2,2,9.27,0.0
H45_B34,45,34,RBF,1,opt1,tw3,3,9.82,0.0 H45_B34,45,34,RBF,1,opt1,tw3,3,9.82,0.0
H45_B34,45,34,RBF,2,opt2,tw1,1,6.81,0.0 H45_B34,45,34,RBF,2,opt2,tw1,1,6.81,0.0
H45_B34,45,34,RBF,2,opt2,tw2,2,9.02,0.0 H45_B34,45,34,RBF,2,opt2,tw2,2,9.02,0.0
H45_B34,45,34,RBF,2,opt2,tw3,3,9.65,0.0 H45_B34,45,34,RBF,2,opt2,tw3,3,9.65,0.0
H45_B34,45,34,Supervised ML,1,opt1,tw1,1,7.34,0.0 H45_B34,45,34,Supervised ML,1,opt1,tw1,1,7.34,0.0
H45_B34,45,34,Supervised ML,1,opt1,tw2,2,9.28,0.0 H45_B34,45,34,Supervised ML,1,opt1,tw2,2,9.28,0.0
H45_B34,45,34,Supervised ML,1,opt1,tw3,3,10.13,0.0 H45_B34,45,34,Supervised ML,1,opt1,tw3,3,10.13,0.0
H45_B34,45,34,Supervised ML,2,opt2,tw1,1,6.87,0.0 H45_B34,45,34,Supervised ML,2,opt2,tw1,1,6.87,0.0
H45_B34,45,34,Supervised ML,2,opt2,tw2,2,9.08,0.0 H45_B34,45,34,Supervised ML,2,opt2,tw2,2,9.08,0.0
H45_B34,45,34,Supervised ML,2,opt2,tw3,3,9.86,0.0 H45_B34,45,34,Supervised ML,2,opt2,tw3,3,9.86,0.0
H45_B34,45,34,Supervised ML,3,opt3,tw1,1,6.84,0.0 H45_B34,45,34,Supervised ML,3,opt3,tw1,1,6.84,0.0
H45_B34,45,34,Supervised ML,3,opt3,tw2,2,9.05,0.0 H45_B34,45,34,Supervised ML,3,opt3,tw2,2,9.05,0.0
H45_B34,45,34,Supervised ML,3,opt3,tw3,3,9.73,0.0 H45_B34,45,34,Supervised ML,3,opt3,tw3,3,9.73,0.0
H60_B34,60,34,RBF,1,opt1,tw1,1,5.98,15.02082 H60_B34,60,34,RBF,1,opt1,tw1,1,5.98,15.02082
H60_B34,60,34,RBF,1,opt1,tw2,2,7.29,15.02082 H60_B34,60,34,RBF,1,opt1,tw2,2,7.29,15.02082
H60_B34,60,34,RBF,1,opt1,tw3,3,8.53,15.02082 H60_B34,60,34,RBF,1,opt1,tw3,3,8.53,15.02082
H60_B34,60,34,RBF,1,opt1,tw4,4,6.73,15.02082 H60_B34,60,34,RBF,1,opt1,tw4,4,6.73,15.02082
H60_B34,60,34,RBF,1,opt1,tw5,5,5.0,15.02082 H60_B34,60,34,RBF,1,opt1,tw5,5,5.0,15.02082
H60_B34,60,34,RBF,2,opt2,tw1,1,5.71,16.67562 H60_B34,60,34,RBF,2,opt2,tw1,1,5.71,16.67562
H60_B34,60,34,RBF,2,opt2,tw2,2,7.44,16.67562 H60_B34,60,34,RBF,2,opt2,tw2,2,7.44,16.67562
H60_B34,60,34,RBF,2,opt2,tw3,3,8.51,16.67562 H60_B34,60,34,RBF,2,opt2,tw3,3,8.51,16.67562
H60_B34,60,34,RBF,2,opt2,tw4,4,6.15,16.67562 H60_B34,60,34,RBF,2,opt2,tw4,4,6.15,16.67562
H60_B34,60,34,RBF,2,opt2,tw5,5,5.0,16.67562 H60_B34,60,34,RBF,2,opt2,tw5,5,5.0,16.67562
H60_B34,60,34,RBF,3,opt3,tw1,1,5.77,17.74124 H60_B34,60,34,RBF,3,opt3,tw1,1,5.77,17.74124
H60_B34,60,34,RBF,3,opt3,tw2,2,7.38,17.74124 H60_B34,60,34,RBF,3,opt3,tw2,2,7.38,17.74124
H60_B34,60,34,RBF,3,opt3,tw3,3,8.37,17.74124 H60_B34,60,34,RBF,3,opt3,tw3,3,8.37,17.74124
H60_B34,60,34,RBF,3,opt3,tw4,4,6.18,17.74124 H60_B34,60,34,RBF,3,opt3,tw4,4,6.18,17.74124
H60_B34,60,34,RBF,3,opt3,tw5,5,5.0,17.74124 H60_B34,60,34,RBF,3,opt3,tw5,5,5.0,17.74124
H60_B34,60,34,Supervised ML,1,opt1,tw1,1,5.97,10.58275 H60_B34,60,34,Supervised ML,1,opt1,tw1,1,5.97,10.58275
H60_B34,60,34,Supervised ML,1,opt1,tw2,2,7.38,10.58275 H60_B34,60,34,Supervised ML,1,opt1,tw2,2,7.38,10.58275
H60_B34,60,34,Supervised ML,1,opt1,tw3,3,8.56,10.58275 H60_B34,60,34,Supervised ML,1,opt1,tw3,3,8.56,10.58275
H60_B34,60,34,Supervised ML,1,opt1,tw4,4,6.7,10.58275 H60_B34,60,34,Supervised ML,1,opt1,tw4,4,6.7,10.58275
H60_B34,60,34,Supervised ML,1,opt1,tw5,5,5.0,10.58275 H60_B34,60,34,Supervised ML,1,opt1,tw5,5,5.0,10.58275
H60_B34,60,34,Supervised ML,2,opt2,tw1,1,5.76,16.96082 H60_B34,60,34,Supervised ML,2,opt2,tw1,1,5.76,16.96082
H60_B34,60,34,Supervised ML,2,opt2,tw2,2,7.37,16.96082 H60_B34,60,34,Supervised ML,2,opt2,tw2,2,7.37,16.96082
H60_B34,60,34,Supervised ML,2,opt2,tw3,3,8.46,16.96082 H60_B34,60,34,Supervised ML,2,opt2,tw3,3,8.46,16.96082
H60_B34,60,34,Supervised ML,2,opt2,tw4,4,6.67,16.96082 H60_B34,60,34,Supervised ML,2,opt2,tw4,4,6.67,16.96082
H60_B34,60,34,Supervised ML,2,opt2,tw5,5,5.0,16.96082 H60_B34,60,34,Supervised ML,2,opt2,tw5,5,5.0,16.96082
H60_B34,60,34,Supervised ML,3,opt3,tw1,1,5.74,16.90444 H60_B34,60,34,Supervised ML,3,opt3,tw1,1,5.74,16.90444
H60_B34,60,34,Supervised ML,3,opt3,tw2,2,7.46,16.90444 H60_B34,60,34,Supervised ML,3,opt3,tw2,2,7.46,16.90444
H60_B34,60,34,Supervised ML,3,opt3,tw3,3,8.5,16.90444 H60_B34,60,34,Supervised ML,3,opt3,tw3,3,8.5,16.90444
H60_B34,60,34,Supervised ML,3,opt3,tw4,4,6.37,16.90444 H60_B34,60,34,Supervised ML,3,opt3,tw4,4,6.37,16.90444
H60_B34,60,34,Supervised ML,3,opt3,tw5,5,5.0,16.90444 H60_B34,60,34,Supervised ML,3,opt3,tw5,5,5.0,16.90444
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